Newton’s Second Law is one of the toughest of the laws to understand but it is very powerful. In its mathematical form, it is so simple, it’s elegant. Mathematically it is F=ma or Force = Mass x Acceleration. An easy way to remember that is to think of your mother trying to get you out of bed in the morning. Force equals MA’s coming to get you! (I did mention how bad physics jokes are, right?)
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Newton’s Second Law
In English, Newton’s Second Law can be stated a few different ways:
The more mass something has and/or the faster it’s accelerating, the more force it will put on whatever it hits. F=ma For example, a car colliding at 30 mph will hit a lot harder then a fly colliding at 30 mph.
The more mass something has, the more force that’s needed to get it to accelerate. a=F/m This, by the way, is a mathematical definition for acceleration. For example, it is a lot harder to get a train to accelerate than it is to get a ping pong ball to accelerate.
So force = mass X acceleration. Let’s try a couple of things and see if we can make that make sense.
Now, time to do an experiment. You will need:
- something slightly slanted, like a slanted driveway or a long board (or even a table propped up on one end)
- something to move down the slant, like a toy car or ball
- a stopwatch
- pen and paper
I’m going to assume you’re using the toy car and a driveway. Feel free to modify the experiment for whatever you are using.
1. Take the toy car to the top of the driveway.
2. Let it go.
3. Watch it carefully as it rolls.
4. If you’d like, you can time the car and mark how far it goes every second like we did in this acceleration experiment.
5. If you time it, measure the distances it went each second and write them down.
Download Student Worksheet & Exercises
What I’m hoping you will see here is that the car accelerates from zero to a certain velocity but then stays at that velocity as it continues down the driveway. In other words, it reaches its terminal velocity. If you timed and marked the distances you should see that the car goes the same distance each second if it is indeed staying at a constant velocity. If the object you are using to roll down the slant, continues to accelerate down the entire ramp, see if you can find something that has more friction to it (a toy car that doesn’t roll quite to easily, for example).
Ok, so what’s going on? F=ma right? Acceleration can’t happen without force. What two forces are effecting the car? (Imagine the Jeopardy theme song here). If you said gravity and friction, give yourself a handshake. When the car is going at a constant velocity, is it accelerating? Nope, acceleration is a change in speed or direction.
“But you just said two forces are effecting my little car and that force causes acceleration and yet my car is not accelerating. Why not?”
Well, there’s one little thing I haven’t mentioned yet, which is why we did this experiment. In this case, the force of gravity pulling on the car and the force of friction pushing on the car is equal (remember, that’s terminal velocity right?). So the net force on the car is zero. The pulling force is equal to the pushing force so there is zero force on the car. Force is measured in Newton’s (name sounds familiar right?) so imagine that there are 3 Newtons of force pulling on the car due to gravity and 3 Newtons of force pushing on the car due to friction. 3 – 3 = 0. Zero force equals zero acceleration because you need force to have acceleration. By the way, 1 Newton is about the same amount of force that it takes to lift a full glass of milk.
Advanced Students: Download your Downhill Races Lab here.
Exercises
- You should notice a difference between these graphs and the ones from the driveway races. What is it? (Hint: look to second half of the graph.)
- The first graph doesn’t continue to curve, but straightens out. What does this mean about the velocity?
- in the second graph, the slope flattens out completely, what does this mean about the acceleration?
- If the acceleration is zero, what does that mean about the net force?
- What are the forces acting on the toy car as it is going down the ramp?
- Name 3 other examples
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